Strong Approximation of Empirical Copula Processes by Gaussian Processes

Salim Bouzebda (1) , Tarek Zari (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.

Mots clés: Gaussian processes; Empirical Copula processes; Strong invariance principles; Kiefer processes; Kernel-type-estimator; Gaussian processes.

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Salim Bouzebda, Tarek Zari. Strong Approximation of Empirical Copula Processes by Gaussian Processes. Statistics, 2013. ⟨hal-00340276v3⟩